Let's talk about varying G

TL;DR

The paper discusses the importance of focusing on dimensionless constants like lpha and lpha_g when studying variations in fundamental constants, highlighting issues with interpreting constraints on G.

Contribution

It emphasizes the need to consider dimensionless combinations of G and mass for meaningful constraints on fundamental constant variations.

Findings

Constraints on G should be expressed as lpha_g, a dimensionless quantity.

Focusing on dimensionless constants clarifies physical interpretations.

Thought experiments can help distinguish measurable variations from unit-dependent effects.

Abstract

It is possible that fundamental constants may not be constant at all. There is a generally accepted view that one can only talk about variations of dimensionless quantities, such as the fine structure constant $\alpha_{\rm e}\equiv e^2/4\pi\epsilon_0\hbar c$. However, constraints on the strength of gravity tend to focus on G itself, which is problematic. We stress that G needs to be multiplied by the square of a mass, and hence, for example, one should be constraining $\alpha_{\rm g}\equiv G m_{\rm p}^2/\hbar c$, where $m_{\rm p}$ is the proton mass. Failure to focus on such dimensionless quantities makes it difficult to interpret the physical dependence of constraints on the variation of G in many published studies. A thought experiment involving talking to observers in another universe about the values of physical constants may be useful for distinguishing what is genuinely measurable from what is merely part of our particular system of units.